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inn [45]
3 years ago
5

Someone please explain step by step.

Mathematics
1 answer:
dolphi86 [110]3 years ago
6 0

Answer:

{10}^{th}  \: term  =  \frac{5}{512}

Step-by-step explanation:

geometric progression formula:

{n}^{th} \:  term  = ar ^{n - 1}

given:

common ratio, r = 1/2

first \: term \:  = 5

1) find the value of a

{n}^{th}  \: term \:  = a {r}^{n - 1}

we're finding the 1st term, so substitute 1 into n:

{1}^{st}  \: term  = a( \frac{1}{2} ) {}^{1 - 1}

first term is 5. so we substitute 5 into the equation:

5 = a(1)

a = 5

2) find the 10th term

we're finding the 10th term, so substitute 10 into the equation and don't forget to substitute 5 into a:

{10}^{th}  \: term  = 5( \frac{1}{2} ) {}^{10 - 1}

{10}^{th}  \: term  = 5( \frac{1}{512} )

{10}^{th}  \: term =  \frac{5}{512}

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Select a value: addition property of equality
Whitepunk [10]

Answer:

Addition prop of equality,    multiplication prop of equality,     multiplication prop. of equality

Step-by-step explanation:

For the first one, we know that in order to solve the equation, we need to add 3 to both sides of the equation. When you add a value to both sides of the equation, you're using the addition property of equality.

For the second one, we know that in order to solve the equation, we need to multiply both side by 1/6 (to cancel the 6 out on the left side). When you multiply something to both sides of the equation, you're using the multiplication property of equality.

For the third one, we know that in order to solve the equation, we must multiply both sides of the equation by 5. Like the second problem, this would be the multiplication property of equality (since you're multiplying both sides of the equation by the same thing).

3 0
3 years ago
A. 3/22 <br> B. 3/7<br> C. 8/15<br> D. 8/11
Oliga [24]
Asked and answered previously.
brainly.com/question/10375997

The appropriate choice is ...
   B. 3/7
8 0
3 years ago
If the radius of the base is 2, and the height is 4, what is the volume of the cylinder?
MAVERICK [17]
givens
pi = 3.14
r = 2
h = 4

Formula
v = pi r^2 h

Sub and Solve
V = 3.14 * 2^2 * 4
V = 3.14 * 4 * 4
V = 3.14 * 16
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4 0
3 years ago
Read 2 more answers
Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation o
hjlf

Answer:

46.18% of the items will weigh between 6.4 and 8.9 ounces.

Step-by-step explanation:

We are given that the weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

<em>Let X =  weight of items produced by a machine</em>

The z-score probability distribution for is given by;

                Z = \frac{  X -\mu}{\sigma}  ~ N(0,1)

where, \mu = mean weight = 8 ounces

            \sigma = standard deviation = 2 ounces

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, percentage of items that will weigh between 6.4 and 8.9 ounces is given by = P(6.4 < X < 8.9) = P(X < 8.9 ounces) - P(X \leq 6.4 ounces)

   P(X < 8.9) = P( \frac{  X -\mu}{\sigma} < \frac{  8.9-8}{2} ) = P(Z < 0.45) = 0.67364  {using z table}

   P(X \leq 70) = P( \frac{  X -\mu}{\sigma} \leq \frac{  6.4-8}{2} ) = P(Z \leq -0.80) = 1 - P(Z < 0.80)

                                                 = 1 - 0.78814 = 0.21186

<em>Now, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.45 and x = 0.80 in the z table which has an area of </em>0.67364<em> and </em>0.78814<em> respectively.</em>

Therefore, P(6.4 < X < 8.9) = 0.67364 - 0.21186 = 0.4618 or 46.18%

<em>Hence, 46.18% of the items will weigh between 6.4 and 8.9 ounces.</em>

8 0
3 years ago
You invest $24,000 at a simple interest rate of 12% for 9 years, and your
FinnZ [79.3K]

Answer:

The principal is $2400

Step-by-step explanation:

Given

P = \$24000

t = 9

r =12\%

I = \$25920

Required

The principal amount

The principal amount is the amount invested.

From the question, we understand that $24000 was invested.

Hence, the principal is $24000

8 0
3 years ago
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